133: Chapter 133 Unfinished Proof in the Side Hall

The room was more spacious than expected.

The floor-to-ceiling glass windows faced the verdant mountain view, with the blackout curtains half-drawn, filtering the scorching afternoon sunlight into a layer of soft gold foil that quietly paved the dark brown solid wood floor.

The central air conditioning panel glowed faintly, preset to a constant, comfortable temperature.

The cool air, carrying the hotel's characteristic faint cedar fragrance, spread indoors, completely blocking out the sticky, humid heat of midsummer Nanjing outside the door.

Jiang Lin leaned his suitcase against the wall, felt in his pocket for his phone, and pulled up the WeChat chat window with his mother, Zhang Xiufen.

"Mom, I have arrived at the hotel."

After a moment of thought, he walked over to the window and snapped a photo of the Zijin Mountain scenery outside.

In the photo, the greenness covering the mountains was illuminated brightly by the sunlight, the branches and leaves of the camphor trees and cedars in the nearby garden intertwined, and beside the distant tree-lined path, a corner of the blue and white ICCM banner fluttering in the wind was faintly visible.

The message was replied to almost instantly.

"It's good that you've arrived."

Less than two seconds later, the next message popped up on the screen.

"Remember to drink more water, and don't stay in the air conditioning all the time."

The next one.

"Nanjing is hot these days, take an umbrella when you go out. Don't always drink iced things, and eat on time."

At the end was a round, system-default sun emoji.

Looking at the admonitions on the screen, Jiang Lin's mouth curved into a tiny arc as he typed quickly.

"I know, you and Dad take care of yourselves too."

After sending the message, he put away his phone.

He placed the document bag on the corner of the desk, unwrapped his badge, and casually hung it on the back of the chair.

He unscrewed a bottle of mineral water, threw his head back, and drank a little less than half the bottle, finally relieving his parched throat a bit.

Awakening his laptop, a few unread messages had already popped up in the work group chat of the Low Entropy Workshop.

Liang Zhixia organized the morning's coordination progress into a streamlined document, marking a non-urgent note next to the title.

Jiang Lin clicked open the document, his gaze swiftly scanning several core project nodes and coordination items, and provided clear approval comments.

Having handled the work, he ate the light meal delivered by room service, leaned back against the sofa, and closed his eyes to rest for a moment.

The quartz clock on the wall pointed to 2:15 PM.

Jiang Lin picked up his phone and tapped on a name in his contacts.

Professor Lin Zhaoye

When the preliminary proof of Jiangs Brick came out back then, the three mentors, Professor Gu Nanzhou, Professor Lin Zhaoye, and Shao Mingtang, were the first to join the verification team.

During that time, Professor Lin Zhaoye had practically postponed all of his original work to help him review local forcing, replacement hierarchies, and boundary classifications layer by layer.

Jiang Lin knew very well that mathematics is a discipline that emphasizes rigor; even without the involvement of the three professors, the correctness of Jiangs Brick would eventually have been confirmed by the academic community, but the process would never have been as calm as it was now, nor would the pace of advancement have been so rapid.

Before coming to Nanjing, he had checked the conference manual, and Professor Lin Zhaoye would also be attending this ICCM.

"Professor Lin, I have arrived at Zijin Villa. Are you free this afternoon? I would like to drop by and visit you."

Less than a minute after the message was sent, the other party replied.

"You've arrived? I am in the side hall of the main venue, right next to the registration desk. No need to rush, rest first."

"I am coming over now."

Another message quickly popped up from the other side.

"Good, don't go around the lobby; taking the second-floor glass corridor from the guest room building is closer."

Jiang Lin put away his phone, took his room card, and closed the door behind him.

Walking down the stairs of the fire exit, he quickly found the glass corridor spanning mid-air.

Outside the corridor was a Chinese-style garden full of Jiangnan charm.

The tall camphor trees and cedars had lush branches and leaves, and the sunlight struggled to penetrate the overlapping gaps, smashing onto the blue-stone slab road below and shattering into patches of light swaying with the wind.

Several small birds perched on the stone railing by the pond, and upon hearing the footsteps coming from the corridor, immediately fluttered their wings alertly and disappeared into the deep shade of the trees.

Every dozen meters along the way stood a blue-and-white signpost.

The arrows pointed clearly to the main venue, various sub-venues, the registration desk, and the tea break area.

The lower right corner of the sign was uniformly printed with the conference logo, consistent with the design language of the roadside banners.

The closer one got to the main venue area, the lower, bustling noises began to blend into the originally quiet air.

Accents from all over, like duckweed floating on the water surface, rippled fine, broken waves with the wind.

Jiang Lin walked past the end of the corridor and entered the side hall of the main venue.

This place felt more like a real academic conference than the hotel lobby.

In the lobby, there was still the hotel's own order—the front desk, concierge, check-in procedures, luggage carts, and shuttling staff—which diluted some of the density of the academic field.

But the side hall was different.

Over a dozen long tables were lined up in a row, and more than a dozen volunteers wearing blue vests were busy with their heads lowered.

Thick document bags, conference badges, the upper and lower volumes of paper abstract collections, schedule booklets, and meal vouchers were piled up like small mountains on the tables.

Quite a few attendees were already queuing up to collect materials; someone who had just received the upper and lower volumes of the paper abstract collections stood in place, furrowing their brows as they flipped through the table of contents.

Someone lowered their head to check the time of a sub-venue.

Others stood in groups of two or three in front of the exhibition boards, resting their suitcases right beside their feet as they began discussing a certain presentation topic.

Jiang Lin walked inward along the edge of the side hall.

Passing the registration desk, a volunteer looked up and saw him, lips parting slightly as if instinctively wanting to remind him to line up for materials, but quickly swallowing the words back after recognizing his badge and face.

Jiang Lin did not stop, his gaze searching through the crowd, and soon spotted Professor Lin Zhaoye in front of a huge schedule exhibition board.

Professor Lin Zhaoye was standing in front of a schedule exhibition board, with two peers beside him.

The three of them seemed to have just concluded a discussion; Professor Lin Zhaoye held conference materials in one hand and pinched a pen with the other, lowering his head to circle a certain position in the schedule booklet.

He appeared slightly thinner than when Jiang Lin last saw him.

His hair was still somewhat messy, glasses perched on the bridge of his nose, and his shirt cuffs rolled up to his forearms, carrying the exhaustion of long-term switching back and forth between blackboards, emails, and proof drafts.

Jiang Lin walked closer and stopped a few steps away.

"Professor Lin."

Professor Lin raised his head.

The moment he saw Jiang Lin, the expression on his face froze slightly at first, and then a gentle smile welled up in the depths of his eyes.

"You have arrived."

Jiang Lin nodded slightly.

"Just arrived at the hotel."

Professor Lin looked him up and down, as if confirming whether a student he hadn't seen in a long time had been worn out on the road.

"Was the trip smooth?"

"Smooth."

"Have you reported to your family?"

Jiang Lin paused for a moment.

"I just sent a message to my mom."

Professor Lin nodded.

"That's good."

Professor Lin exchanged a few brief words with the two companions beside him.

The two of them had actually already recognized Jiang Lin, but out of scholars' tacit understanding, they did not rashly step forward to interrupt.

Hearing that Professor Lin Zhaoye was going to sit down with Jiang Lin, the two naturally yielded space for conversation.

Before leaving, one of the scholars deliberately nodded toward Jiang Lin: "Congratulations, that single-brick paper is exceptionally elegant."

Jiang Lin responded politely: "Thank you."

After the people had walked away, Professor Lin Zhaoye pointed to a relatively secluded resting area in the corner of the side hall.

The two took their seats at a spot against the floor-to-ceiling window.

A row of tall green plants acted as a natural screen, moderately separating this space from the bustling registration desk.

The commotion on the periphery could still be heard, but it was less dense.

Professor Lin Zhaoye suddenly asked: "Coming to a convention like this for the first time, how does it feel?"

Jiang Lin thought for a moment and gave an objective evaluation: "The environment is quite nice."

Professor Lin smiled, then put aside his casual demeanor and asked about PFR and Marton.

"Don't tell me that was just a prospective metaphor?"

Jiang Lin fell silent for a moment.

Outside the side hall, human voices still flowed in low tones.

Volunteers checked names at the registration desk, attendees dragged suitcases past from a distance, and people occasionally stopped to take photos in front of the schedule exhibition board.

This was not a place suitable for discussing proofs.

But Professor Lin Zhaoye asked very directly.

Jiang Lin did not pretend not to understand either.

"It's not a metaphor."

"If it's not a metaphor, what does that mean?"

Jiang Lin said: "On the side of the Finite Field Model, the main proof has been closed."

Professor Lin Zhaoye raised his head abruptly.

Looking at Jiang Lin, it was as if he was judging whether this sentence was the arrogance of a youth or a mathematician's calm description of their proof status.

In a few seconds of silence, the commotion outside suddenly seemed very far away.

Professor Lin Zhaoye asked slowly: "When you say closed, do you mean you've found a possible route, or do you mean the key lemmas have all been connected?"

"The key lemmas are connected."

"What about the covering number?"

"Polynomial level, didn't drop back to exponential."

Professor Lin Zhaoye's pupils contracted slightly.

He no longer leaned back against the sofa, but slowly sat straight.

"Finite Field PFR?"

"Yes."

"What about Marton?"

"Bridging through entropy forms. The complete version still needs to be organized."

"Organized, what do you mean?"

"The current draft allows me to confirm the logical closure myself, but it cannot yet let others review efficiently," Jiang Lin said. "The symbol system is too heavy, and the third-layer loss recovery still needs to be re-compressed. Bringing it out directly would cause reviewers to be drowned in technical details first rather than seeing the structure."

Professor Lin Zhaoye stared at him.

This sentence carried even more weight than 'I have proved it.'

Because Jiang Lin did not show any excitement eager to announce a breakthrough.

When speaking of an extremely terrifying matter, he still used the tone of organizing a proof draft.

Being able to confirm logical closure oneself.

But not yet able to let others review efficiently.

This was neither inspiration nor conjecture, let alone a pretty tail thrown out at the end of a report to attract attention.

Rather, it was someone who had already completed the internal closure of the main proof, considering how to transform it from something he could understand into something the community could re-verify.

Professor Lin Zhaoye suddenly felt his throat feel a bit dry.

Giangs Brick was already astonishing enough.

At eighteen, single-brick aperiodic tiling ended half a century of core questioning.

That was already an achievement sufficient for a young mathematician to be written into the footnotes of the history of mathematics.

But PFR / Marton was not Jiangs Brick.

It was not a problem where an elegant construction was found and then pushed to the end through rigorous verification.

It spanned Additive Combinatorics, entropy methods, approximate structures, and high-dimensional Finite Field Models.

What it affected was the underlying way of understanding the entire direction.

More importantly, how long had it been since the ICM?

The moment Jiang Lin said there was a way at the end of his report at the ICM, many people still thought it was just the usual ambition of a young genius.

Yet here he was sitting now, saying to himself that the main proof had been closed.

Professor Lin Zhaoye slowly took off his glasses and pressed hard on the space between his eyebrows.

This action was very brief.

So brief it was almost as if due to exhaustion.

But Jiang Lin could tell that was not exhaustion.

That was the reaction of a mature mathematician trying to forcibly suppress instinctive shaking in an extremely short time.

Professor Lin Zhaoye put his glasses back on, and his first sentence was not congratulations.

But asked: "How many people have seen it?"

"It hasn't been made public yet."

"What about Professor Han Yanshan?"

"No."

"Professor Gu Nanzhou?"

"Nor him."

Professor Lin Zhaoye pondered for a moment and said in a low voice: "Then you shouldn't have said so much here just now."

Jiang Lin said: "I didn't talk about the details either."

"You've already said enough."

Professor Lin Zhaoye glanced at the crowd outside the side hall.

"Jiang Lin, from now on, before closing the door and confirming the personnel present, do not say the word 'closed' to anyone else."

"I understand."

Professor Lin Zhaoye looked at him, his gaze holding shock, doubt, and excitement.

Even more, a sense of powerlessness almost akin to absurdity.

He had originally thought that after Jiangs Brick, Jiang Lin would at least go quiet for a period of time.

Organizing verification materials, attending the ICM, attending the ICCM, dealing with external clamor.

Handling the Low Entropy Workshop, and then slowly returning to mathematics.

But looking at it now, the clamor seen by the outside world hadn't truly touched Jiang Lin's core progress at all.

The youth built robots in the mud and built firewalls between capital and media.

At the same time, on another even more incredible route, he had actually pushed the main proof of PFR / Marton toward the finish line.

At this thought, Professor Lin Zhaoye suddenly smiled.

"You brat, really..."

Professor Lin Zhaoye originally wanted to say 'truly awesome', but before the words left his mouth, he found that any simple 'awesome' seemed too light in front of this matter.

Right at this moment, a voice came from outside the resting area.

"Professor Lin."

The two raised their heads simultaneously.

A middle-aged man in his forties walked over from the other side of the side hall.

He was not tall, wore a light blue short-sleeved shirt, had a conference guest badge hanging in front of his chest, and held a conference schedule booklet in his hand.

Seeing him, Professor Lin Zhaoye's expression was not surprised.

"Professor Han."

The other party first nodded to Professor Lin Zhaoye, and then his gaze fell on Jiang Lin.

"Jiang Lin?"

"Professor Han."

Jiang Lin stood up.

Professor Han Yanshan reached out and shook hands with him.

"I originally planned to find you for a chat a bit later, but just now I heard at the registration desk that you had arrived, so I came straight over."

Professor Han Yanshan was a straightforward person without any transition.

"At the end of your forty-five-minute report at the ICM, you mentioned PFR and Marton."

Regarding what Jiang Lin said at the end of those 45 minutes at the ICM, when spreading to the outside world, most people only regarded it as his proof of setting his sights on a great mountain once again.

It was a signal.

An eighteen-year-old youth who had just solved the single-brick problem said at the end of his ICM report that he had a few thoughts about that mountain.

Others could smile and exclaim that youths really dare to think.

But Professor Han Yanshan did not.

He deeply cultivated this field and knew well that the terminology Jiang Lin chose on that occasion was definitely not spoken casually.

"I want to ask, the thoughts you mentioned—are they a philosophical analogy, or do they already have a technical route that can be substantially pushed forward?"

Professor Lin Zhaoye did not chime in.

Jiang Lin did not hesitate either, replying directly: "Not a pure analogy."

Professor Han Yanshan's gaze changed noticeably, and his breathing suddenly grew hurried.

"Can we talk about it?"

Jiang Lin looked around and said: "The current occasion is not quite suitable."

Professor Han Yanshan immediately realized the noisy environment and nodded decisively: "Of course, mathematics requires quiet."

Jiang Lin was about to speak when his phone vibrated first.

A message came from the conference organizing committee's exclusive notification number.

"Dear Mr. Jiang Lin, Mr. Qiu will be hosting a small casual dinner at the Zijin Hall at 7:00 tonight, and would like to invite several young scholars to dine together. If it is convenient for you, please reply to confirm, and we will reserve a seat for you."

Jiang Lin finished reading the message and looked up.

"At 7:00 tonight, the conference organizing committee has an arrangement."

Professor Lin Zhaoye glanced at his expression and quickly reacted.

At a convention of this level, very few could make the conference organizing committee specifically send such an invitation.

"Mr. Qiu's side?"

Jiang Lin nodded.

Hearing this name, Professor Han Yanshan, who had originally wanted to finalize the subsequent time, immediately swallowed back the words that reached his lips.

Even if he had hundreds or thousands of questions in his heart, he would never let Jiang Lin turn down Shing-Tung Yau's small casual dinner.

Everyone knew clearly that for a young scholar like Jiang Lin who had just been pushed into the spotlight of the mathematical community, this was also the formal beginning of close observation by a certain core circle.

Professor Lin Zhaoye stood up opportunely and said: "Let's talk about it later then; Jiang Lin has just arrived, and his chair hasn't even warmed up yet. Let's not keep blocking him here."